The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A352166

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A352166

Number of partitions of n into distinct odd prime powers (1 included).
(history; published version)

#7 by Michel Marcus at Mon Mar 07 12:58:28 EST 2022

STATUS

reviewed

approved

#6 by Joerg Arndt at Mon Mar 07 11:11:58 EST 2022

STATUS

proposed

reviewed

#5 by Ilya Gutkovskiy at Mon Mar 07 09:41:30 EST 2022

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Mon Mar 07 09:40:38 EST 2022

FORMULA

G.f.: Product_{k>=0} (1 + x^A061345(k)).

STATUS

proposed

editing

#3 by Ilya Gutkovskiy at Sun Mar 06 16:27:21 EST 2022

STATUS

editing

proposed

Discussion

Mon Mar 07

09:38

Michel Marcus: add formula for Mma program ?

#2 by Ilya Gutkovskiy at Sun Mar 06 16:18:16 EST 2022

NAME

allocated for Ilya GutkovskiyNumber of partitions of n into distinct odd prime powers (1 included).

DATA

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 4, 5, 6, 6, 6, 7, 8, 9, 9, 10, 12, 12, 13, 14, 16, 17, 17, 19, 21, 23, 23, 25, 28, 30, 31, 33, 37, 38, 40, 43, 47, 50, 52, 55, 60, 64, 66, 70, 76, 81, 83, 89, 96, 101, 105, 110, 119, 125, 130, 138, 147, 155, 161

OFFSET

0,9

MATHEMATICA

nmax = 70; CoefficientList[Series[Product[(1 + Boole[(PrimePowerQ[k] || k == 1) && OddQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000961, A024939, A054685, A061345, A106244, A134337, A280152, A352165.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Mar 06 2022

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sun Mar 06 16:18:16 EST 2022

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved